In [1]} Sims could explain the limited correlation between the behavior of economic agents and the information they have access to, observing the information through a rate limited channel. One application for this novel way of viewing/modeling economic agents is to solve the permanent income problem where there is limited information about the labour as well as the wealth, which is a dynamic programming problem with mutual information constraint on the state information of the system. In [2]}, [3]} the concept of information constrained dynamic programming is brought into the context of multi-agent coordination. Agents are limited to local observations but are allowed to communicate through rate-limited channels. Therein, the authors have developed a state aggregation algorithm which enables each agent to compress its generated communication message while maintaining their performance in the collaborative task. Similarly in [4]}, authors introduce task-based joint source channel coding to solve the problem of multiagent coordination over noisy communication channels.
To understand how these works are relevant to our framework, it should be noticed that, in fact, the information constraint on the observation of the agents in the aforementioned works can be translated as the limitation of on the communication channel between the observer of the environment and the controller.
